The present invention relates generally to protective relaying, and more particularly to a method and apparatus for use in connection with a protective relay or like device to accurately measure the impedance of a power system transmission line.
In a power distribution system, electrical transmission lines and power generation equipment must be protected against faults and consequent short circuits. Otherwise, such faults and short circuits can cause a collapse of the system, equipment damage, and/or personal injury. Accordingly, and as shown in FIG. 1, a typical power system employs one or more protective relays to monitor impedance and other AC voltage and current characteristics on a protected transmission line, to sense faults and short circuits on such protected line, and to appropriately isolate such faults and short circuits from the remainder of the power system by tripping pre-positioned circuit breakers on such protected line.
As seen, a typical power system can be connected over hundreds of miles and include multiple power generators (generator S, generator R) at different locations. Transmission lines (the main horizontal lines in Fig. 1) distribute power from the generators to secondary lines or buses (the main vertical lines in Fig. 1), and such buses eventually lead to power loads. Importantly, relays and circuit breakers are appropriately positioned to perform the isolating function described above.
A modern protective relay typically records voltage and current waveforms measured on a corresponding protected line, and employs a memory and microprocessor and/or digital signal processor (DSP) to process the recorded waveforms and to estimate impedance and voltage and current phasors based on such processed waveforms. As should be understood, a voltage or current phasor expresses the respective parameter in terms of its magnitude and phase angle. As used herein, the term xe2x80x98transmission linexe2x80x99 includes any type of electrical conductor, such as a high power conductor, feeder, transformer winding, etc. Based on the estimated impedance and voltage and current phasors, the protective relay can then decide whether to trip an associated relay, thereby isolating a portion of the power system.
In particular, and referring now to FIG. 1A, it is seen that a typical protective relay 10 samples voltage and current waveforms VA, VB, VC, IA, IB, IC from each phase (A-C) of a three phase line 12. Of course, greater or lesser numbers of phases in a line may be sampled. The sampled waveforms are stored in a memory 14 and are then retrieved and appropriately operated on by a processor or DSP 16 to produce the aforementioned estimated impedances and phasors. Based thereon, the relay 10 may then decide that an associated circuit breaker 18 should be tripped to isolate a portion of the line 12 from a fault condition or from other detected phenomena, and issue such a command over a xe2x80x98TRIPxe2x80x99 output (xe2x80x98TRIP 1xe2x80x99 in Fig. 1A) that is received as an input to the circuit breaker 18. The relay 10 may then reset the circuit breaker after the relay 10 senses that the fault has been cleared, or after otherwise being ordered to do so, by issuing such a command over a xe2x80x98RESETxe2x80x99 output (xe2x80x98RESETxe2x80x99 1 in FIG. 1A) that is received as an input to the circuit breaker 18.
Notably, the relay 10 may control several circuit breakers 18 (only one being shown in FIG. 1A), hence the xe2x80x98TRIP 2xe2x80x99 and xe2x80x98RESET 2xe2x80x99 outputs. Additionally, the circuit breakers 18 may be set up to control one or more specific phases of the line 12, rather than all of the phases of the line 12. Owing to the relatively large distances over which a power system can extend, the distance between a relay 10 and one or more of its associated circuit breakers 18 can be substantial. As a result, the outputs from the relay 10 may be received by the circuit breaker(s) 18 by way of any reasonable transmission method, including hard wire line, radio transmission, optical link, satellite link, and the like.
As seen in FIGS. 1 and 2, transmission lines may oftentimes be series-compensated by series capacitance 20 that includes one or more capacitors or banks of capacitor installations (a representative series capacitor CAP is shown). Benefits obtained thereby include increased power transfer capability, improved system stability, reduced system losses, improved voltage regulation, and better power flow regulation. However, such installation of series capacitance introduces challenges to protection systems for both the series-compensated line and lines adjacent thereto.
In particular, series compensation elements installed within a power system introduce harmonics and non-linearities in such system. Particularly when using waveform-type algorithms (i.e., algorithms that rely on current and voltage waveforms to determine a parameter of interest) to estimate impedance and voltage and current phasors, several transient problems may cause very large errors. Such voltage and current phasors are employed in relaying applications, for example, to determine whether a fault is in a protected zone. It is imperative, then, that such phasor estimates be as accurate as possible in view of installed series capacitance. Examples of the aforementioned transient problems that may cause very large errors include:
DC Offsetxe2x80x94In uncompensated and compensated power systems, a fault current waveform will contain an exponentially decaying DC offset component in addition to a fundamental frequency. The amount of the DC offset is dependent on the fault inception angle and system parameters such as network configuration, number and length of transmission lines, compensation percentage, power flow, generator and transformer impedances, etc. A variety of algorithms have been devised to compensate for DC offset. Some algorithms use a differentiation technique that eliminates the effect of the DC offset and ramp components in the fault current waveform. Mimic circuits and cosine filters have also been employed.
Sub-Synchronous Frequenciesxe2x80x94On series-compensated lines, series capacitance introduces a sub-synchronous frequency which is dependent on capacitance value and various system values. When a fault occurs, the fault current waveform includes two sinusoids, one oscillating at the predetermined system frequency (50 Hz, 60 Hz, etc.), and the other at the system natural frequency (neglecting system resistance and load current). The system natural frequency is determined by the degree of compensation, the source impedance, and the distance to fault location, among other things. Accordingly, a higher system natural frequency occurs when a fault is closer to a respective relay. The higher frequency will not be as critical for close-in faults since a metal oxide varistor (MOV) associated with the series capacitance (shown in FIG. 2 in parallel with the representative series capacitor (CAP)) will typically short the capacitance in such a situation. However, when a fault occurs farther out from a relay toward the end of a line, the lower system natural frequency will cause the aforementioned voltage and current phasor estimates to oscillate. Such oscillation affects the real and imaginary components of the phasor estimations, resulting in a xe2x80x98cloudxe2x80x99 effect. For most power systems, installed series capacitance results in a sub-synchronous harmonic component in the fault current waveform. The impact of high frequency components in the fault current waveform is usually reduced by low-pass filters in the relay.
MOV and Overload Protection Operationxe2x80x94Once a fault has occurred, a bypass breaker or bypass switch (SW) (shown in FIG. 2 in parallel with the representative series capacitor) closes following operation of an overload protection system. Typically, and as seen, the breaker is controlled by a protective relay 10 via an appropriate BYPASS output (FIG. 1A). Typically, and as shown in FIG. 2, bypassing the installed capacitance in actuality causes an inductance (L) to be placed in parallel with the installed capacitance to form a damping circuit. Accordingly, the closing of such breaker introduces a transient in the system as the breaker arcs and the impedance seen by the relay is altered. As a result, the impedance to the fault increases and the fault current decreases, thus altering the phasor estimates. The quick response of the MOV and overload protection (the spark gap (SG) shown in FIG. 2 in parallel with the representative series capacitor) removes or reduces the capacitance and limits the impact of the sub-frequency component.
Accordingly, a need exists for an impedance measurement system that operates accurately in connection with a power system transmission line, particularly in view of harmonics and non-linearities introduced by installed series compensation elements.
The present invention satisfies the aforementioned need by providing an accurate impedance measurement method for a power system transmission line. The invention provides improvements to various protection functions, i.e., distance protection and/or fault location estimation. The inventive method is less sensitive than conventional methods to harmonics and other transient problems introduced to power systems by series capacitance and the like. Moreover, existing protective relays can easily incorporate the method in their protection functions, so that the improvements can be achieved with minimal cost.
In the method, a number (n) of current and voltage samples (Ik, Vk) representative of values of current and voltage waveforms are measured, respectively, at successive instants of time on a conductor in a power system. The number n is an integer greater than 1 and the index k takes on values of 1 to n. Resistance (R) and inductance (L) values are computed in accordance with an equation in which R and L are related to sums of differences in values of successive current and voltage samples. A prescribed power system function is then performed based on the computed R and L values.